A386446 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^5 * a(k) * a(n-1-k).

1, 1, 2, 67, 16414, 16840826, 52661283276, 409599480216723, 6884957718009061046, 225620064835937122627934, 13323090455565480199133495252, 1332335691963961772604470940370302, 214576660211223693770379106296061734124, 53393968668333658608864584261609697870131860

Offset: 0

Author

Seiichi Manyama, Jul 22 2025

Keywords

• nonn

Crossrefs

Cf. A075834, A386443, A386444, A386445, A386447.

Cf. A385833.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, j^5*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x - x*Sum_{k=1..5} Stirling2(5,k) * x^k * (d^k/dx^k A(x)) ).